When you say prevent Watergate do you mean that it doesn't happen at all or that it simply isn't discovered? The latter is much easier to do since all it take is a slightly less observant night guard or bribing one of them to look the other way. Alternatively if you don't want it to occur at all have Nixon eke out a win in the 1962 California gubernatorial election, the satisfaction of winning, and being able to throw it in the media's faces, helps him mellow out slightly. He's still going to be Richard Nixon, with all that entails, but he realises that the Democrats don't represent a serious threat to him for 1972 so either doesn't authorise the break-ins and bugging or calls them off much sooner when it's shown they're not providing anything of value.